IICQI-20 talk: Probing the quantumness of states and channels with truncated moment sequences

The "entanglement problem" is to decide whether a given quantum state of a composite system is entangled over a chosen partition or not. We show that it can be mapped to the "truncated moment problem", for which recently a complete solution was found in the sense of a necessary and sufficient condition. It gives rise to a hierarchy of semi-definite programs corresponding to state extensions with polynomial constraints, and the positive-partial-transpose criterion as a first step, that generalizes and unifies on an abstract level previous approaches such as the Doherty-Parrilo-Spedalieri hierarchy. The approach is very flexible and can, in particular, accomodate naturally missing experimental data, symmetries, and subsystems of different dimensions.

We then apply the machinery of truncated moment sequences to tackle an important experiment-design problem, namely how to best choose a sequence of measurements for showing as quickly as possible that a state is separable withoug having to reconstruct the full state.

Finally, we make a step towards the quantumness-certification of quantum processors by extending the approach to the quantumness of channels.